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Stability in asymmetric Hopfield nets with transmission delays. (English) Zbl 0815.92001

Summary: Sufficient conditions are derived for the delay independent stability of the equilibria in Hopfield’s graded response networks of the type

dx i (t)/dt=-b i x i (t)+ j=1 n a ij f j μ j x j (t-τ ij )+F i (t)(i=1,2,,n)

when the external inputs F i are held temporally uniform. A generalization to continuously distributed delays is briefly indicated. Several illustrative examples are numerically simulated and the results of simulations are graphically displayed.

MSC:
92B20General theory of neural networks (mathematical biology)
34D99Stability theory of ODE